Many genes, RNAs and proteins are present in such extremely low numbers that random collisions between individual molecules create fluctuations in abundances between otherwise identical cells. The sources and dynamics of such 'noise' have been analyzed in detail, for example showing how variances respond to changes in transcription and translation as expected from models of stochastic gene expression. Preliminary mathematical theory surprisingly suggests a very different explanation, showing that almost all such results are equally consistent with fluctuations that instead originate due to unequal partitioning of molecules at cell division. Other mathematical results suggest that random partitioning of molecules indeed could contribute at least as much as gene expression to the overall heterogeneity. These results motivate a broad experimental investigation of segregation, comparing stochastic partitioning for different types of macromolecules: in-depth analyses of active segregation mechanisms of plasmids in Escherichia coli, a quantification of proteolysis in E. coli, and an mRNA and protein survey in Schizosaccharomyces pombe. Each system was chosen because of the key principles illustrated, because of the central roles they play biologically and threats they pose clinically, and because new experimental approaches developed in the lab make it possible to analyze them much more quantitatively. The experimental analyses go hand-in-hand with both analytical toy models of basic principles, general nonlinear mathematical theory that collectively addresses classes of cyclic random processes. In addition to analyzing and comparing central biological systems in molecular and kinetic detail, this ambitious proposal could produce a substantial shift in the quantitative perspective on fluctuations in cellular constituents, and will provide several enabling mathematical and experimental methods. The processes studied are also relevant to human health both by studying a central principle important to all cell growth and division, and by focusing on specific systems of clinical relevance, such as the genes responsible for the majority of antibiotic resistance outbreaks, and the protective responses of pathogenic bacteria.